Subdividing a face with subdivided edges
As a general rule you should avoid ngons and triangles.



To deal with the big and ugly ngon in the center of the screen,  select opposing vertices and Join them with using vertex connect: Press the  J key.





Then do that on the cross section.

Then get rid of all of the triangles and ngons and make every possible effort to use quads.





For some ideas on how to deal with changing topology see Johnson Martin's page on:

http://topology-guides.tumblr.com/

An example from that page: